First off, this is a great question to ask! Secondly, all of contractors that answered are absolutely correct - each and every answer.
Every company goes about leveraging the costs of projects differently. From a consumer perspective, I would look for a sliding scale. For instance, if the project is a $30,000 kitchen remodel, expect to give a 25% down payment to initiate the contract. However, kitchen remodels can move very fast depending how prepared you are prior to the start of the construction process; so, for this example, I would expect to have all $30,000 ready for release of payment within 2-3 weeks from beginning to end.
Also, down payments are good for the consumer and the contractor. For instance, a down payment of $7,500 from the example above will be applied to labor costs because the GC will have a demo crew, dumpster, permit and rough material to purchase and leverage with the $7,500 down payment. But, it is not always about down payments; it is more about financial flexibility.
It is important to have financial flexibility during a project. If you would like to expedite the project, then you should partner with the GC to purchase material in advance. This money can be included in the contract and removed as purchased, or you can exclude it from the contract and purchase material independently. Either way, it is important as a consumer to understand that having finances prepared prior to entering the project makes the project that much easier to navigate and manage and expedite for both the consumer and the GC.